Temperature and Thermal Expansion: Understanding Heat and Coldness

1. Chapter 5 Temperature and Heat

2. Temperature • Temperature is loosely defined as a measure of the hotness or coldness of a substance. • This is a very subjective definition. • We will provide a better definition, shortly. • There are three common temperature scales: • Kelvin, • Celsius, and • Fahrenheit.

3. Temperature, cont’d • The temperature scales can be compared by examining the freezing and boiling points of water. • These are determined by the atomic structure of water. • We must do the comparisons at the same pressure since theses phase transitions depend on pressure. • Especially the boiling point.

4. Temperature, cont’d • This figure illustrates the relative values of the three temperature scales.

5. Temperature, cont’d • We define absolute zero as the coldest temperature. • It is better defined as the temperature at which all the random motion of matter is halted. • The lowest value on the Kelvin scale is absolute zero. • So, 0 K corresponds to absolute zero. • This is -273.15°C or -459.67°K.

6. Temperature, cont’d • The freezing point of water is defined to be 0°C. • This corresponds to 32°F and 273 K. • The boiling point of water is defined to be 100°C. • This corresponds to 212°F and 373 K. • Note that the Kelvin scale is the only scale that is never negative. • There is an absolute English scale: Rankine.

7. Temperature, cont’d • To convert from Celsius to Fahrenheit: • To convert from Fahrenheit to Celsius:

8. Temperature, cont’d • Here is a more definitive definition of temperature: • The Kelvin temperature of matter is proportional to the average kinetic energy of the constituent particles. • This helps explain many phenomena that we will examine. • It explains why the pressure of a gas increases as the gas’ temperature increases.

9. Temperature, cont’d • As the temperature increases, the average KE of the particles increases. • The average speed of the particles increases. • At higher temperatures, when the atoms collide with the container walls they impart more momentum — the strike with a larger force.

10. Thermal expansion • We know that the average KE of atoms increases with high temperature. • We saw what this means for gases. • The pressure increases as the temperature rises. • What about solids? • The solid’s atoms are not free to move like in a gas. • But they can vibrate.

11. Thermal expansion, cont’d • Consider a rod that has a length l. • Now heat the rod. • The atoms begin to vibrate more since their KE increases. • Since they are bound to a fixed position, the simply vibrate with a larger amplitude.

12. Thermal expansion, cont’d • The result is that the rod gets longer. • This depends on: • The length of the rod l; • The change in temperature, DT; and • The substance.

13. Thermal expansion, cont’d • We can write this mathematically as • Dl is the change in the rod’s length, • a is the coefficient of linear expansion and has units of 1/°C, • l is the rod’s initial length (before the temperature change), and • DT is the change in temperature.

14. ExampleExample 5.1 The center span of a steel bridge is 1,200 meters long on a winter day when the temperature if -5°C. How much longer is the span on a summer day when the temperature is 35°C?

15. ExampleExample 5.1 ANSWER: The problem gives us: The change in temperature is: The change in length is

16. ExampleExample 5.1 DISCUSSION: This is a change of almost two feet. Engineers compensate for this by providing expansion joints, as shown.

17. Thermal expansion, cont’d • A bimetallic strip is commonly used in devices that need to monitor temperature. • Two dissimilar metals are bonded together. • They have different coefficients of thermal expansion. • One metal expands more with a given temperature change than the other. • The strip bends.

18. Thermal expansion, cont’d • An analog thermostat is a common example of a bimetallic strip.

19. Thermal expansion, cont’d • Liquids also undergo thermal expansion with a temperature increase. • We typically deal with the volume expansion. • Consider water as a “special” example. • A volume of water increases with an increase in temperature above 4°C. • Between 0° and 4°C, water contracts with an increase in temperature. • Water is most dense at 4°C.

20. Thermal expansion, cont’d • Gases also expand with an increase in temperature. • For a given pressure, the volume of a gas is proportional to its temperature: • This means that if you heat a balloon, the volume will increase. • It is (almost) constant pressure since the balloon is capable of expanding.

21. Thermal expansion, cont’d • Instead of a balloon, consider a gas in a metal container of fixed volume, e.g., a can of beans. • The pressure, volume and temperature are related through: • Heating the can increases the pressure. • Get the can hot enough, it will explode.

22. Thermal expansion, cont’d • What if we let the pressure, volume and temperature change? • These three quantities are related through the ideal gas law: • This is the general statement from which the previous cases are special examples.

23. First law of thermodynamics • So far, we have discussed only one way to increase an objects temperature: • expose it to something that has a higher temperature. • There is another possibility: • Do work on it.

24. First law of thermodynamics, cont’d • Consider piston pushing on a gas in a cylinder. • Forcing the piston down requires a force. • Applying this force through a distance means you are doing work. • The work is done against the gas. • You compress the gas. • The gas gets hot.

25. First law of thermodynamics, cont’d • A diesel engine uses this concept. • The diesel/air mixture is compressed in the cylinder. • At maximum compression the mixture ignites. • The pressure increase from the explosion pushes the piston down. • This causes the crankshaft to turn.

26. First law of thermodynamics, cont’d • Compressing a gas increases its temperature. • We noted last chapter that temperature is related to the average kinetic energy of the gas atoms/molecules. • So compressing the gas increases its internal energy.

27. First law of thermodynamics, cont’d • Internal energy is the sum of the kinetic and potential energies of all the atoms and molecules in a substance. • Internal energy is represented by the symbol U. • For gases, we only deal with the kinetic energy part of the internal energy. • The particles interact only during collisions, which is infrequent.

28. First law of thermodynamics, cont’d • Heat is a form of energy that is transferred between two substances because they have different temperatures. • An object does not have heat. • An object transfers heat when its temperature is raised by contact with a hotter object or lowered by contact with a cooler object. • Heat is represented by the symbol Q.

29. First law of thermodynamics, cont’d • The First Law of Thermodynamics states that the change in internal energy of a substance equals the work done on it plus the heat transferred to it:

30. First law of thermodynamics, cont’d • Recall that work can be positive or negative. • When a gas is compressed, positive work is done on the gas. • The change in internal energy is positive — the gas’ internal energy increases. • When a gas expands, negative work is done on the gas. • The change in internal energy is negative — the gas’ internal energy decreases.

31. First law of thermodynamics, cont’d • Internal energy is important during phase transitions. • When you boil water, you increase the water’s temperature and its internal energy. • As the water undergoes the phase change to water vapor, its internal energy increases but its temperature remains at 100°C. • The energy added to the water to evaporate is applied to break the bonds holding the molecules together — not to the molecular kinetic energy.

32. Explorations in Physics Lecture 4 — Nov. 7, 2005 Chapters 5.4 – 6.6

33. Heat transfer • There are three types of heat transfer: • Conduction: the transfer of heat between atoms and molecules in direct contact. • Convection: the transfer of heat by buoyant mixing in a fluid. • Radiation: the transfer of heat by way of electromagnetic waves.

34. Heat transfer — conduction • Heat is conducted across the boundary between two substances. • For a pan on a stove, the conduction occurs because the flame is in contact with the bottom of the pan. • Conduction also occurs within the pan. • The bottom gets hot and makes the top hot.

35. Heat transfer — conduction • Thermal insulators are materials through which energy is transferred slowly. • Wool is a good thermal insulator because it contains large amounts of trapped air that slow down the transfer of energy. • Thermal conductors are materials through which energy is transferred quickly. • Metals are good thermal conductors because they contain electrons that are free to move throughout the material.

36. Heat transfer — conduction • A hard-wood floor feels colder than a carpeted floor because the wood conducts heat more quickly from your foot than the carpet. • You can judge a good conductor if it feels colder than another substance at the same temperature.

37. Heat transfer — convection • Convection is also responsible for much of the weather pattern. • During the day, the ground warms more quickly than the water. • The cooler air moves-in to replace the warmer air that rose. • During the night, the water retains its heat longer than the ground. • The cooler air above the ground moves to replace the warmer air that rose above the water.

38. Heat transfer — radiation • Radiation is the transfer of heat via electromagnetic waves. • You feel the “heat” of a light bulb because of: • The bulb radiates some of its energy as visible light and some as infra-redheat. • The bulb warms the air through conduction. • The warm air rises through convection.

39. Specific heat capacity • Transferring heat to/from a substance changes its internal energy. • The substance’s change in temperature for a given change in internal energy depends on the type of substance. • It requires much more energy to raise the temperature of water than of air.

40. Specific heat capacity, cont’d • The amount of heat transferred to a substance is proportional to the substance’s change in temperature: • The amount of heat transferred to accomplish a certain temperature change depends on the mass of substance: • More mass means more particles to absorb the added energy.

41. Specific heat capacity, cont’d • The amount of heat transferred to accomplish a certain temperature depends on the type of material: • We use the specific heat capacity, C, to represent the amount of energy required to raise 1 kg of a substance’s temperature by 1°C.

42. Specific heat capacity, cont’d • Here is a table of some specific heat capacities.

43. Specific heat capacity, cont’d • Recall that heat is a transfer of energy. • So we use joules as a unit for heat. • Historically, the unit of a calorie was used for heat. • It was a revolutionary idea that heat and energy are equivalent. • The conversion between joules are calories:

44. ExampleExample 5.2 Let’s compute how much energy it takes to make a cup of coffee or tea. Eight ounces of water has a mass of about 0.22 kilograms. How much heat must be transferred to the water to raise its temperature from 20°C to the boiling point, 100°C?

45. ExampleExample 5.2 ANSWER: The problem gives us: The temperature change is The heat transferred is

46. ExampleExample 5.2 DISCUSSION: This is approximately the same energy required to accelerate a pickup to a speed of nearly 30 mph.

47. ExampleExample 5.3 A 5-kilogram concrete block falls to the ground from a height of 10 meters. If all of its original potential energy goes to heat the block when it hits the ground, what is its change in temperature?

48. ExampleExample 5.3 ANSWER: The problem gives us: The potential energy of the block is:

49. ExampleExample 5.3 ANSWER: This energy equals the heat transferred to the block: The temperature change is found from

50. ExampleExample 5.3 ANSWER: The resulting temperature change is